From this answer https://physics.stackexchange.com/a/196166/147599 I have read that when we are free falling, the fictitious force cancels out the gravity pull so we'll feel no force. Would the fictitious force still be present if we stand on the ground? I mean, with our own reference frame, we are still not accelerating.Or is it the normal force that cancels out the weight? if so, do we feel double the upwards force than gravity (F(up)=2mg)?
No, the observer will not feel a fictitious force when he is on the ground. Remember, fictitious forces arise when a reference frame accelerates relative to an inertial frame. When the observer is falling, he is accelerating towards the ground, so his reference frame accelerates with him. This acceleration then causes his instruments to register a spurious (fictitious) acceleration. When the observer is on the ground, he is not moving, and neither is his reference frame. So there is no fictitious force.
You are correct that the normal force cancels the gravitational one in all reference frames.